Question 1
What is the maximum value of an expression 
5
−
8
+
7
×
4
−
8
+
9
5−8+7×4−8+9 that can be obtained by placing pairs of parentheses into it? For example, 

(
(
5
−
8
)
+
7
)
×
4
−
8
+
9
=
17
 
,
((5−8)+7)×4−8+9=17,
 

(
5
−
(
8
+
7
)
)
×
(
4
−
(
8
+
9
)
)
=
130
 
.
(5−(8+7))×(4−(8+9))=130

To maximize the value of the expression \(5 - 8 + 7 \times 4 - 8 + 9\) by strategically placing parentheses, let's analyze how each part of the expression can contribute to the maximum result.

### Step 1: Original Expression
The expression is:
\[
5 - 8 + 7 \times 4 - 8 + 9
\]

### Step 2: Evaluate Without Parentheses
If we evaluate it as written, following standard order of operations (multiplication before addition and subtraction), we get:
\[
5 - 8 + (7 \times 4) - 8 + 9 = 5 - 8 + 28 - 8 + 9 = 26
\]

### Step 3: Try Different Parentheses Combinations
Now, let's try various ways of grouping terms with parentheses to maximize the result:

1. **\(((5 - 8) + 7) \times 4 - 8 + 9\)**
   - Evaluate inside the parentheses: \((5 - 8) + 7 = -3 + 7 = 4\)
   - Then multiply: \(4 \times 4 = 16\)
   - Final result: \(16 - 8 + 9 = 17\)

2. **\((5 - (8 + 7)) \times (4 - (8 + 9))\)**
   - Evaluate inside the parentheses: \(5 - (8 + 7) = 5 - 15 = -10\) and \(4 - (8 + 9) = 4 - 17 = -13\)
   - Then multiply: \((-10) \times (-13) = 130\)
   - Final result: \(130\)

This second setup, \((5 - (8 + 7)) \times (4 - (8 + 9))\), yields a result of **130**, which is higher than any other grouping configuration.

### Conclusion
The maximum value of the expression, achieved by using parentheses as \((5 - (8 + 7)) \times (4 - (8 + 9))\), is:
\[
\boxed{130}
\]

Do you need further explanation on any part of this solution?

---

### Related Questions:
1. How does the order of operations affect the value of an expression?
2. What are other methods for maximizing expressions with multiple operations?
3. Can this method be applied to expressions with exponents or roots?
4. What is the minimum possible value of this expression with parentheses?
5. How do parentheses impact expressions with more variables?

### Tip:
When working with complex expressions, always evaluate potential groupings with parentheses to explore maximum and minimum values systematically.

What is the maximum value of an expression 5−8+7×4−8+9 that can be obtained by placing pairs of parentheses into it? For example, ((5−8)+7)×4−8+9=17, (5−(8+7))×(4−(8+9))=130.

Learn how to maximize the expression 5−8+7×4−8+9 by strategically placing parentheses. This problem involves key concepts in order of operations and expression maximization, using methods to achieve the highest possible result. Suitable for students in Grades 8-10.

Math Problem Statement

( ( 5 − 8 ) + 7 ) × 4 − 8 + 9

( 5 − ( 8 + 7 ) ) × ( 4 − ( 8 + 9 ) )

Solution

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